Conical square function estimates in UMD Banach spaces and applications to H-infinity functional calculi

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dc.creatorHytonen, Tuomas
dc.creatorvan Neerven, Jan
dc.creatorPortal, Pierre
dc.date2007-09-10
dc.date.accessioned2026-07-07T12:27:49Z
dc.date.available2026-07-07T12:27:49Z
dc.descriptionWe study conical square function estimates for Banach-valued functions, and introduce a vector-valued analogue of the Coifman-Meyer-Stein tent spaces. Following recent work of Auscher-McIntosh-Russ, the tent spaces in turn are used to construct a scale of vector-valued Hardy spaces associated with a given bisectorial operator (A) with certain off-diagonal bounds, such that (A) always has a bounded (H^{\infty})-functional calculus on these spaces. This provides a new way of proving functional calculus of (A) on the Bochner spaces (L^p(\R^n;X)) by checking appropriate conical square function estimates, and also a conical analogue of Bourgain's extension of the Littlewood-Paley theory to the UMD-valued context. Even when (X=\C), our approach gives refined (p)-dependent versions of known results.
dc.description28 pages; submitted for publication
dc.identifierhttps://arxiv.org/abs/0709.1350
dc.identifierhttp://arxiv.org/abs/0709.1350
dc.identifierJ. Anal. Math. 106(1): 317-351 (2008)
dc.identifierdoi:10.1007/s11854-008-0051-3
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/215338
dc.subjectFunctional Analysis
dc.subjectSpectral Theory
dc.subject46B09 (Primary); 42B25, 42B35, 46B09, 46E40, 47A60, 47F05 (Secondary)
dc.titleConical square function estimates in UMD Banach spaces and applications to H-infinity functional calculi
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